Doughnut P.

asked • 11/25/14# Factoring using GCF

So this Section is "solving quadratic equations by factoring", I got the hang of it, but stumped on a few. So one problem says 8y^2 -28y-60 and the answer is 4(2y+3)(y-5). I do not get how they got that though. Because for other problems like 5x^2+5x-10 I came up with 5(1x^2+1x-2) and it seems legit (Did it according to how a site taught iT)

Also troubled on 3x^2+54x+243. The GCF is 3, so I do 3(1x^2+18x+81). Either thats it or I break it down to 3(1x+2x)(1x+9).

Thanks.

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## 2 Answers By Expert Tutors

Mark M. answered • 11/25/14

Tutor

5.0
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Mathematics Teacher - NCLB Highly Qualified

8y

^{2 }- 28y - 60, factor out common factor of "4"4 ( 2y

^{2}- 7y - 15 ), factor using FOIL4 ( 2y + 3 )( y - 5 )

Following that patter,

5x

^{2 }- 5x - 105 ( x

^{2}- x - 2 )5 ( x -2 )( x + 1)

You are correct to "break it down" for the third one.

Doughnut P.

Thank you for confirming, although I do not understand how it gets down to 3(1x=2x)(1x+9) on the last one. Or is this not so? What I got prior to this was 3(1x+6x)(1x+27).

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11/25/14

Mark M.

x

^{2 }+ 18x + 81 is a perfect square trinomial; a^{2}+ 2ab + b^{2}= (a + b)^{2}x2 + 18x + 81 = (x + 9)

^{2}
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11/25/14

8y

^{2 }-28y -60we can start by looking for any factor that is common in all terms

The number 4 is a factor of each term so we can factor it out

4(2y

^{2}- 7y -15)OK now we have to find the factors of the first and last terms of the binomial and figure out which combination will give us the middle term

factors of 2y

^{2}are 2y and y

factors of -15

-1 and 15

1 and -15

-3 and 5

3 and -5

now we can try combinations of these factors to get -7 in the middle

I will leave it to you to try different combinations but the correct combination is 3 and -5

becasue 2y times -5 gives -10y and y times 3 gives 3y and the combination gives -7y

so our factors are

4(2y+3)(y-5)

hope this helps

Doughnut P.

This one makes much more sense. Thanks.

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11/25/14

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Doughnut P.

^{2}-3x+2. I got it into intercept form but it is incorrect.11/25/14